CN110680308A - ECG signal denoising method based on fusion of improved EMD and threshold method - Google Patents

Abstract

The invention proposes an electrocardiographic signal denoising method based on the fusion of improved EMD and threshold method, and belongs to the technical field of signal filtering. The invention solves the modal aliasing problem by superimposing white noises of different weight coefficients, solves the end point problem by the method of least squares support vector machine, constructs the upper and lower envelopes of the signal by the method of conformal spline interpolation, and uses conformal segmentation. The method can construct cubic spline interpolation with second-order approximation accuracy, less segmentation and less computation. This method can suppress the problem of overshoot/undershoot of envelope fitting. The orthogonality and energy properties of the decomposed IMFs , put forward the criterion for the termination of "sieving" of IMF components, which ensures the orthogonality and completeness of EMD decomposition. The principle of mutual information is used to determine how much noise the sieved IMF signal contains to decide whether to filter it or not. , which increases the rapidity of the EMD algorithm; improves the threshold function, which combines the advantages of soft and hard thresholds to filter IMFs containing noise.

Description

ECG signal denoising method based on fusion of improved EMD and threshold method

technical field

The invention relates to a method for denoising an electrocardiogram signal, in particular to a method for denoising an electrocardiogram signal based on the fusion of improved EMD and a threshold method, and belongs to the technical field of signal filtering.

Background technique

ECG signal is a typical non-stationary and weak bioelectric signal, which is widely used in the diagnosis and treatment of various heart diseases. The ECG signal is often accompanied by very serious high-frequency and low-frequency noise, and the noise frequency band often overlaps with the ECG signal frequency band, so filtering and preprocessing are difficult.

Traditional biomedical signal processing is mainly based on Fourier theory. Fourier signal processing technology is almost irreplaceable in signal spectrum analysis and its associated data compression, signal detection, filtering and other signal processing fields. However, the integral interval of Fourier transform is from positive infinity to negative infinity, and it cannot obtain the spectral content of the signal in a certain period of time. The wavelet transform has become an effective method for processing biomedical signals such as ECG because of its excellent time-frequency analysis characteristics and the ability to process non-stationary random signals. Similarly, EMD has also begun to be applied to the field of biomedical processing due to its good adaptability in analyzing nonlinear and non-stationary signals. Such as electrocardiogram signal analysis, blood pressure signal denoising, heartbeat signal analysis, etc., have been successfully applied.

Empirical mode decomposition (EMD) decomposes the signal into the sum of a finite number of intrinsic mode functions (IMF). The EMD decomposition fully considers the local scale features of the signal itself, and each IMF component obtained in this way represents a scale feature of the original signal and contains the real physical information of the original signal. As a new adaptive signal time-frequency processing method, EMD has been widely used in mechanical fault diagnosis, feature extraction, geophysical detection, medical analysis, etc., and the EMD method has also been extended to the field of two-dimensional signal processing. It has been well applied in the fields of less image edge detection, texture analysis, image fusion, image compression, image filtering, etc., which all illustrate the effectiveness of EMD.

There are still some shortcomings in the current EMD method and further research is needed. Such as: research on EMD fast algorithm, EMD modal aliasing problem, end effect, signal envelope fitting problem and IMF component "sieve" termination criterion research. The quality of the envelope curve fitting in the method directly affects the decomposition results. The original method of using cubic spline function interpolation is completed with extreme points as known points. Because of the uneven distribution of extreme points, it leads to It is the fitting of non-uniform points, which will cause the problem of extreme undershoot or overshoot, resulting in a larger error of decomposition. Mode aliasing is a problem often encountered in the use of EMD, which is mainly caused by discontinuous events and signal interaction.

Aiming at the above-mentioned defects, the present invention proposes an ECG signal denoising method based on the fusion of improved EMD and threshold method, aiming to improve the quality of ECG signal empirical mode decomposition and improve the effect of noise removal.

SUMMARY OF THE INVENTION

In view of the deficiencies in the prior art, the purpose of the present invention is to propose an improved fusion technology of EMD and threshold method, so as to complete the decomposition of the ECG signal and remove the noise of the ECG signal. The invention solves the modal aliasing problem by superimposing white noises of different weight coefficients, solves the end point problem by the method of least squares support vector machine, constructs the upper and lower envelopes of the signal by the method of conformal spline interpolation, and uses conformal segmentation. This method can suppress the problem of overshoot/undershoot of envelope fitting, and avoid the interpolation error caused by the traditional interpolation method with the decomposition process. The errors that occur as the continuous process continues to accumulate. Based on the orthogonality and energy properties of the decomposed IMFs, the criterion for the termination of "sieving" of the IMF components is proposed, which ensures the orthogonality and completeness of the EMD decomposition. The principle of mutual information is used to determine how much noise the filtered IMF signal contains to decide whether to filter it, which greatly increases the speed of the EMD algorithm. An improved threshold function is proposed, which combines the advantages of soft and hard thresholds to filter IMFs containing noise.

The invention aims to solve the problem of modal aliasing caused by using EMD decomposition, and proposes an electrocardiographic signal denoising method based on the fusion of improved EMD and threshold method.

An ECG signal denoising method based on the fusion of improved EMD and threshold method, comprising the following steps:

Step 1: Improved EMD decomposition of ECG signal;

Step 1.1: The method of adding white noise to the ECG signal can be expressed as:

代表对心电信号第a次加入正系数白噪声后的信号；

代表对心电信号第a次加入与正系数相对应的负系数白噪声后的信号；y(t)代表心电信号；n(t)代表均值为零，单位方差的白噪声；ω_a为权重系数。以下步骤1.2～1.5是加入正系数白噪声的处理方法，加入负系数白噪声的处理方法与此类似，仅需将上标“+”改为“-”，含义表示与之对应的加入负系数白噪声的情况。in,

Represents the signal after adding positive coefficient white noise to the ECG signal for the a-th time;

Represents the signal after adding the negative coefficient white noise corresponding to the positive coefficient to the ECG signal for the ath time; y(t) represents the ECG signal; n(t) represents the white noise with zero mean and unit variance; ω _a is weight factor. The following steps 1.2 to 1.5 are the processing method of adding positive coefficient white noise, and the processing method of adding negative coefficient white noise is similar to this, only need to change the superscript "+" to "-", which means that the corresponding negative coefficient is added. case of white noise.

进行采样，信号采样序列为

N为采样点数。训练样本集为A＝{(h₁,g₁),(h₂,g₂),···,(h_l,g_l)}，其中：h_i为输入向量，

g_i为输出向量，

1≤i≤l；l为训练样本集个数；测试样本集B＝{(h_N-S+1,g_N-S+1),(h_N-S+2,g_N-S+2),···,(h_N,g_N)}，其中：1≤S为测试样本数；Step 1.2: In order to avoid divergence at both ends during signal interpolation and fitting, that is, end point effect. Extend the two ends of the signal by using the least squares support vector machine; sample the signal processed in step 1.1, first, for

For sampling, the signal sampling sequence is

N is the number of sampling points. The training sample set is A={(h ₁ ,g ₁ ),(h ₂ ,g ₂ ),...,(h _l ,g _l )}, where: h _i is the input vector,

g _i is the output vector,

1≤i≤l; l is the number of training sample sets; test sample set B={(h _N-S+1 , g _N-S+1 ), (h _N-S+2 , g _N-S+2 ),...,(h _N ,g _N )}, where: 1≤S is the number of test samples;

其中，

为延拓后的第一个信号，再将作为原始数据新的边界点，以同样的方法得到第2个数据序列延拓值

以此类推，根据需要延拓数据点的个数可以得到全部延拓序列其中，M为向右延拓的信号点数，对于给定数据序列向左延拓的方法与向右延拓的方法相同，并记向左延拓的序列为：

最终延拓后的序列记为 With the test sample set, the output of the least squares support vector machine is

in,

is the first signal after extension, and then As the new boundary point of the original data, the second data sequence extension value is obtained in the same way

By analogy, all the extended sequences can be obtained by extending the number of data points as needed. Among them, M is the number of signal points extended to the right. For a given data sequence, the method of extending to the left is the same as the method of extending to the right, and the sequence of extending to the left is recorded as:

The final extended sequence is denoted as

Step 1.3: Construct the upper and lower envelopes of the signal by means of conformal spline interpolation.

Step 1.3.1: Determine whether the point is an extreme point by comparing the magnitude relationship between a point in the sequence Z(t _i ) obtained in step 1.2 and its left and right neighboring points. The specific operations are as follows:

时：When judging endpoint .. with

Time:

则点

为极大值点。like

then point

is the maximum point.

like then point is the minimum point.

为极大值点。like then point

is the maximum point.

则点

为极小值点。like

then point

is the minimum point.

When judging points other than the above endpoints:

-M+1≤i≤N+M-1，则点

为极大值点。like

-M+1≤i≤N+M-1, then point

is the maximum point.

-M+1≤i≤N+M-1，则点

为极小值点。like

-M+1≤i≤N+M-1, then point

is the minimum point.

的极大值点序列为：The sequence can be obtained by the above method

The maximum point sequence of is:

{x _max (t ₀ ),x _max (t ₁ ),...,x _max (t _b )}, where b is the number of maximum points;

The sequence of minimum points is:

{x _min (t ₀ ),x _min (t ₁ ),...,x _min (t _c )}, where c is the number of maximum points.

Step 1.3.2: Construct the upper envelope through the maximum points.

Insert two numerical points between every two maximum points, defined as follows:

where t _ij is the j-th insertion point between times t _i-1 and t _i .

The sequence after inserting the numerical points is:

{x _max (t ₀ ), x _max (t ₁₁ ), x _max (t ₁₂ ), x _max (t ₁ ), x _max (t ₂₁ ), x _max (t ₂₂ ), x _max (t ₃ ), ...,x _max (t _b )}

Taking the above sequence as the control vertex of the T-B spline curve, the upper envelope, namely the T-B spline curve, can be expressed as follows:

Among them, j represents the fitted j-th TB spline curve; U represents the upper envelope; h _ij (t) is the TB spline basis function. When fitting the curve from t ₀ to t ₁ , h _ij (t ) is expressed as follows:

in:

When fitting t ₁ : t ₂ , t ₂ : t ₃ , ···, t _b-1 : t _b segment curves, the expression of h _ij (t) is similar to the above.

Step 1.3.3: Construct the lower envelope through the minimum value points. The construction method is similar to the method of constructing the upper envelope. The expression of the lower envelope is as follows:

Among them, D represents the lower envelope;

Step 1.4: Find the mean of the upper and lower envelopes:

Among them, m _a (t) is the mean value of the upper and lower envelopes obtained after adding positive coefficient white noise for the ath time;

与m_a(t)的差值：Calculate the signal

Difference from m _a (t):

为第a次加入正系数白噪声经第i次EMD分解的IMF；剩余量

If C(t) does not meet the IMF definition cut-off condition, repeat step 1.3; otherwise extract C(t) as

is the IMF decomposed by the i-th EMD after adding positive coefficient white noise for the a-th time;

Step 1.5: Take the remaining amount r(t) of step 1.4 as a new signal, that is, r(t)=y(t), and then filter through steps 1.1 to 1.4 to obtain the next lower frequency IMF, until If the screened IMF components satisfy the following rules, the screening is stopped.

The stopping criterion for the termination of IMF component "sieving" is:

Where: IMF _i (t) is the IMF of the i-th EMD decomposition, and n is the length of IMF _i (t);

When ZSD<θ, stop sieving, preferably, θ=0.03.

Step 1.6: The decomposed signal can be expressed as the following formula:

为第a次加入正系数白噪声经第i次EMD分解的IMF，r_d(t)为进行第d次分解时的残差。Among them: d is the number of IMFs decomposed by EMD of the ECG signal,

is the IMF decomposed by the i-th EMD after adding positive coefficient white noise for the a-th time, and r _d (t) is the residual when the d-th time decomposition is performed.

Similar to steps 1.1 to 1.5, calculate the EMD decomposition after adding negative coefficient white noise to the ECG signal. The decomposed signal can be expressed as the following formula:

为第a次加入负系数白噪声经第i次EMD分解的IMF。in,

It is the IMF decomposed by the i-th EMD after adding the negative coefficient white noise for the a-th time.

Step 1.7: Accumulate and average the IMFs obtained in step 1.6 after adding positive and negative coefficient white noises, to obtain:

in:

Step 2: Determine the linear relationship between each IMF and the original signal by arranging mutual information, and determine the effective signal of the IMF obtained in Step 1. The formula is as follows:

QI(IMF ^(k) ,y)=S(IMF ^(k) )+S(y)-S(IMF ^(k) ,y) (13)

Among them: S(IMF ^(k) ) and S(y) are the permutation entropy of IMF ^(k) (t) and y(t) respectively, and the calculation formula of S(IMF ^(k) ) is as follows:

where p( ) represents the joint probability density of permutation ( ), which is calculated as follows:

为IMF^(k)的一个状态向量，对应的排列是(π_i)；排列(π_i)表示时间序列IMF^(k)(t)映射到d维空间后每个状态向量所对应的一个排列顺序；where i=1,2,...,n-(d-1)τ, n is the length of the time series, d is the given embedding dimension, τ is the time delay; # represents the number of elements in the set,

is a state vector of IMF ^(k) , and the corresponding arrangement is (π _i ); arrangement (π _i ) represents an arrangement order corresponding to each state vector after the time series IMF ^(k) (t) is mapped to the d-dimensional space ;

Assuming that the time series {IMF ^(k) (t)} is mapped to the d-dimensional phase space, the joint state vector is defined as:

Its state vector is used to represent the trajectory of the i-th time sequence. Through this definition, the trajectory state matrix mapped to the state space can be obtained:

By comparing the size relationship of the neighbor values of the row vector of each state matrix to obtain an arrangement order, the arrangement matrix of the trajectory matrix can be obtained:

S(y) is calculated similarly to S(IMF ^(k) ).

S(IMF ^(k) ,y) represents the joint arrangement entropy of IMF ^(k) (t) and y(t), and the calculation formula is as follows:

where p(π _i , π _j ) represents the joint probability density of permutations (π _i , π _j ), and the calculation formula is as follows:

where the subscript i'=1,2,...,n-(d-1)τ, A pair of state space trajectory matrices, the corresponding arrangement is (π _i , π _j ); the arrangement (π _i , π _j ) indicates that the time series of IMF ^(k) (t) and y(t) are mapped to the d-dimensional space. An arrangement order corresponding to the state vectors is represented as follows: Assuming that the time series {IMF ^(k) (t)} and {y(t)} are mapped to the d-dimensional phase space, the joint state matrix is defined as:

Its state vector is used to represent the trajectory of the i-th time sequence. Through this definition, the trajectory-like matrix mapped to the state space can be obtained:

By comparing the size relationship of the neighbor values of the row vector of each state matrix to obtain an arrangement order, the arrangement matrix of the trajectory matrix can be obtained:

According to the mutual information QI value of each IMF and the original signal, the degree of interference of each IMF by noise is judged. The more noise, the smaller the QI value. The IMFs with obviously small QI values are selected for denoising.

Step 3: Perform threshold denoising processing on the IMFs selected in step 2 that need to be denoised. The threshold formula is as follows:

可调参数α为正数，可调参数m为正数；阈值λ₁的计算公式如下：Where: Tunable parameter

The adjustable parameter α is a positive number, and the adjustable parameter m is a positive number; the calculation formula of the threshold λ ₁ is as follows:

σ为各个IMF分量中噪声标准差，σ＝median(IMF_i)/0.6745，median(·)为求中位数；threshold

σ is the noise standard deviation in each IMF component, σ=median(IMF _i )/0.6745, median( ) is the median;

The calculation formula of the threshold λ ₂ is as follows:

Step 4: The remaining IMFs in step 2 are reconstructed with the signal processed in step 3. The calculation formula is as follows:

Among them, y'(t) represents the denoised signal.

So far, from step 1 to step 4, a process of ECG signal denoising based on the fusion of improved EMD and threshold method is completed.

beneficial effect

An ECG signal denoising method based on the fusion of improved EMD and threshold method, compared with the prior art, the method has the following beneficial effects:

1. This method adopts the method of adding positive and negative white noise with different weight coefficients for multiple times, which effectively solves the modal aliasing problem caused by the interaction of two signals in EMD, and improves the frequency resolution of the algorithm (here Said frequency resolution refers to the ability to distinguish two adjacent frequency components);

2. This method uses the least squares support vector machine method to extend and add windows to the signal, which avoids the distortion phenomenon that occurs when the signal is decomposed by using the cubic spline interpolation method to fit the signal;

3. This method uses the shape-preserving spline interpolation method to construct the upper and lower envelopes of the signal. This method uses the shape-preserving segmentation method to construct the cubic spline interpolation method with second-order approximation accuracy, less segmentation and less computation to suppress the signal. The envelope fitting overshoot/undershoot problem avoids the interpolation error caused by the traditional interpolation method and the continuous accumulation of errors as the decomposition process continues, resulting in serious errors.

4. This method directly uses the threshold method to denoise the IMF, which effectively reduces the operation time. And improve the threshold function, the threshold function better retain the details and edge characteristics of useful signals, on the basis of realizing signal noise reduction, better propose effective signals, ensure the amplitude of the signal, and improve the denoising effect, Reduced operation time.

5. The method has a simple process and is easy to implement, and can be used in the design of related software in the field of electrocardiographic signal analysis.

Description of drawings

Fig. 1 is the step schematic diagram of the present invention;

Fig. 2 is the flow chart of the present invention;

Fig. 3 is the detailed schematic diagram of EMD decomposition of the present invention;

Detailed ways

The present invention will be described in detail below according to the accompanying drawings and examples, but the specific embodiments of the present invention are not limited thereto.

The data in this example comes from patient sampling data from the Department of Cardiovascular Medicine, General Hospital of the Chinese People's Liberation Army. The ECG is used to collect ECG signals from the patient. The signal duration is 5s and the sampling frequency is 360Hz. ) in the context of ECG data.

This embodiment describes the process of applying the "ECG signal denoising method based on the fusion of improved EMD and threshold method" of the present invention to an ECG signal denoising scenario.

Figure 1 is a schematic diagram of the steps of the method, and Figure 2 is a specific flow chart. It can be seen from the figure that the ECG signal is collected first, and then the following steps are performed:

Step A: carry out improved EMD decomposition to the collected signal; Fig. 3 is a detailed schematic diagram of the EMD decomposition of the present invention, which is specifically as follows:

Step A1: Add positive ω ₁ times white noise n(t) with zero mean and unit variance to the collected signal y(t);

Specifically to this embodiment, the amplitude of the white noise is 0.05 times the standard deviation of the ECG signal, that is, ω ₁ =0.5, and the signal after adding noise is denoted as x ₁ (t);

Step A2: use the least squares support vector machine to extend the x ₁ (t) signal obtained in step A.1;

Sampling x ₁ (t) to get the sampling sequence {x(1), x(2), x(3), . . . , x(N)}, N is the number of sampling points, and the training sample set is B={( h ₁ ,g ₁ ),(h ₂ ,g ₂ ),...,(h _l ,g _l )}.

Specifically, in this embodiment, the number of sampling points is 2000 and the number of training samples is 100, so the training samples can be obtained: the input samples are 100×1900 dimensional data.

The first prediction value extended to the right is x(N+1); then x(N+1) is used as the new boundary point of the original data, and the second data sequence extension value x(N) is obtained in the same way +2). By analogy, according to the need to extend the number of data points, all the extended sequences x(N+1), x(N+2)..., x(N+M) can be obtained. For a given data sequence, the forward continuation The method is the same as the method of backward continuation.

Extending 100 sampling points from the two ends of the signal to both sides, that is, M=100, the extended sequence is: {x(1),x(2),x(3),...,x(2200) }.

Step A3: Construct the signal envelope using the method of conformal spline interpolation;

Specifically to this embodiment, it is determined whether the point is an extreme point by comparing the size relationship between each point in the sequence obtained in step A.2 and its left and right neighboring points. According to the comparison rule, the compared maximum value sequence is {x _max (t ₀ ),x _max (t ₁ ),...,x _max (t _b )}, where b is the number of maximum points; by formula (2), insert two points between the two maximum points The value is used as the control vertex of the TB spline, and the upper envelope of the signal is constructed by formula (3), which is denoted as The method of constructing the lower envelope is similar to that of the upper envelope, denoted as

Step A4: use formula (6) to calculate the mean value m _a (t) of the upper and lower envelopes;

Step A5: use formula (7) to calculate the difference between the signal x ₁ '(t) obtained in step A.2 and the mean value m _a (t);

计算剩余量，并使剩余量为原始信号，重复步骤A1—步骤A5，直到剩余分量为单调函数时停止筛分。According to formula (8), judge whether C(t) satisfies the definition cut-off condition of IMF, that is, when ZSD<0.3, then extract C(t) as IMF; otherwise, use formula

Calculate the remaining amount, and make the remaining amount the original signal, repeat steps A1 to A5, and stop sieving until the remaining component is a monotonic function.

Step A6: Change the weighting factor ω of Step A.1, and perform the sieving of Steps A.1 to A.5 m times;

Specifically to this embodiment, the white noise amplitude can be 0.05 times, 0.06 times and 0.04 times the standard deviation of the ECG signal, adding a total of 100 times;

Step A7: use formula (12) to obtain all IMF components of the signal decomposed by EMD;

Step B: judging the effective signal of each IMF obtained by arranging the mutual information;

Step B1: Find the permutation entropy of the time series;

Specifically to this embodiment, the embedding dimension is 1001, and the time delay is 1. According to the Shannon entropy of the permutation probability density function, the permutation entropy S(IMF ^(k) ) and S(y) of the time series IMF ^(k) (t) and y(t) are calculated; the joint time series is calculated by formula (18). The joint permutation entropy S(IMF ^(k) ,y) of (IMF ^(k )(t),y(t)).

Step B2: utilize formula (13) to calculate permutation mutual information;

Step B3: Judging the degree of interference of each IMF by noise according to the mutual information QI value of each IMF and the original signal, the greater the amount of noise, the smaller the QI value. The IMFs with obviously small QI values are selected for denoising.

Step C: perform threshold denoising processing on the IMFs selected in step B that need to be denoised;

Specifically to this embodiment, the selected IMFs are denoised by using the formula (23).

Step D: The remaining IMFs in Step B are reconstructed with the signal processed in Step C.

The signal is reconstructed by equation (24).

So far, from step A to step D, an ECG signal denoising method based on the fusion of improved EMD and threshold method in this embodiment has been completed.

Claims (10)

1. An electrocardiographic signal denoising method based on the fusion of improved EMD and threshold method, comprising the steps: A. Perform an improved EMD decomposition on the acquired signal, specifically: A1. Add positive coefficient white noise n(t) with zero mean and unit variance of ω _a times to the collected signal y(t) to obtain the signal

The subscript a means adding white noise for the ath time; A2. Use the least squares support vector machine to pair the signal The two ends are extended to obtain the extended sequence; A3. Construct the upper envelope of the continuation sequence by means of conformal spline interpolation

and lower envelope

j represents the jth segment TB spline fitting curve; A4. Calculate the mean value of the upper and lower envelopes obtained after adding white noise for the ath time and signal

Difference from m _a (t)

If C(t) does not meet the cut-off condition defined by IMF, repeat step A3; otherwise, extract C(t) as Represents the IMF decomposed by the i-th EMD after adding the positive coefficient white noise for the a-th time; calculate the residual amount

A5. Use the remaining amount r(t) of step A4 as a new signal, that is, r(t)=y(t), and then filter through steps A1 to A4 to obtain the next lower frequency IMF until it is screened out The IMF component of satisfies ZSD<θ, then stop the sieving, where θ is the set threshold, and the ZSD calculation formula is:

IMF _i (t) is the IMF of the ith EMD decomposition, and n is the length of IMF _i (t); A6. The signal decomposed by A1~A5 is expressed as

Among them, d is the number of IMFs after the ECG signal is decomposed by EMD,

is the IMF decomposed by the i-th EMD after adding positive coefficient white noise for the a-th time, and r _d (t) is the residual during the d-th decomposition; Similar to steps A1 to A5, EMD decomposition is performed on the ECG signal after adding negative coefficient white noise, and the decomposed signal is expressed as

in,

is the IMF decomposed by the i-th EMD after adding the negative coefficient white noise for the a-th time; A7. Accumulate and average the IMF obtained in step A6 after adding positive coefficient and negative coefficient white noise to obtain

in,

B. Judging the linear relationship between each IMF and the original signal by arranging mutual information, and judging the effective signal of the IMF obtained in step A; C. Perform threshold denoising processing on the IMFs selected in step B that need to be denoised; D. The remaining IMFs in step B are reconstructed with the signal processed in step C. 2. The method for denoising an ECG signal according to claim 1, wherein the A2 comprises:

The sampling sequence is obtained by sampling as

N is the number of sampling points; through the test sample set, the output of the least squares support vector machine is

in,

is the first signal after extension;

As the new boundary point of the original data, the second data sequence extension value is obtained

And so on, according to the need to extend the number of data points to get all the extended sequence

Among them, M is the number of signal points extended to the right; for a given data sequence extended to the left, we get

The final extension sequence is

3. The method for denoising an ECG signal as claimed in claim 1 or 2, wherein the A3 comprises: comparing the magnitude relationship between a certain point in the continuation sequence and its left and right adjacent points to determine whether the point is a pole or not Value points; construct the upper envelope through the maximum value points

Construct the lower envelope through the minimum points

4. The method for denoising an ECG signal as claimed in claim 3, wherein the method for judging whether the point is an extreme point: for an endpoint

and

like

then point

is the maximum point, otherwise, the point

is the minimum point; if

then point is the maximum point, otherwise, the point

is the minimum point; For points other than the above endpoints: if

then point

is the maximum point; if

then point

is the minimum point, where -M+1≤i≤N+M-1. 5. The method for denoising an ECG signal according to claim 1, wherein the step B comprises: B1. Calculate the permutation entropy S(IMF ^(k) ) and S(y) of the time series IMF ^(k) (t) and y(t); B2. Calculate permutation mutual information; B3. According to the mutual information QI value of each IMF and the original signal, the degree of interference of each IMF by noise is judged, and the IMF with the smaller QI value is selected for denoising processing. 6. The electrocardiographic signal denoising method according to claim 1 or 5, wherein the calculation formula of the arrangement mutual information is: QI(IMF ^(k) ,y)=S(IMF ^(k) )+S(y)-S(IMF ^(k) ,y), where S(IMF ^(k) ) and S(y) are IMFs respectively ^(k) The permutation entropy of (t) and y(t), S(IMF ^(k) , y) is the joint permutation entropy of IMF ^(k) (t) and y(t). 7. ECG signal denoising method as claimed in claim 6, is characterized in that, the calculation formula of the arrangement entropy of described S (IMF ^(k) ) is:

where p(·) represents the joint probability density of permutations (·). 8. The electrocardiographic signal denoising method according to claim 6, wherein the calculation formula of the joint arrangement entropy S(IMF ^(k) ,y) of the IMF ^(k) (t) and y(t) for Among them, the arrangement (π _i , π _j ) represents an arrangement order corresponding to each state vector after the IMF ^(k) (t) and y(t) time series are mapped to the d-dimensional space, and the joint probability density Subscript i'=1,2,...,n-(d-1)τ,

is a pair of state-space trajectory matrices whose corresponding permutations are (π _i ,π _j ). 9. The electrocardiographic signal denoising method according to claim 1, wherein the threshold calculation formula in the step C is:

Among them, the adjustable parameter m is a positive number, and the adjustable parameter

α is a positive number,

σ is the noise standard deviation in each IMF component, σ=median(IMF _i )/0.6745, median( ) is the median;

10. The method for denoising an ECG signal according to claim 1, wherein the signal reconstruction calculation formula in the step D is:

Among them, y'(t) represents the denoised signal.

Images